= Surjective rational Hurewicz homomorphism gives a wedge of spheres
If $X$ is <simply connected> and $h_*:\pi_*(X)\otimes\mathbb Q\to\widetilde H_*(X;\mathbb Q)$ is onto, choose a homogeneous <homology> <basis> and representing sphere maps into $X_{\mathbb Q}$. Their <wedge sum> gives a <rational homology> equivalence, hence a <rational homotopy equivalence> by the <rational Whitehead theorem>. All positive <cup products> therefore vanish. In a <minimal model>, the induced map from <cohomology> to the indecomposable quotient is injective; replacing a set of generators by cocycle representatives produces a <quasi-isomorphism> to the square-zero <cohomology> algebra, proving <formality of a topological space>.
Back to article page
